Joint BCAM-UPV/EHU Analysis and PDE seminar: The Vlasov-Poisson-Boltzmann/Landau equation with polynomial perturbation near Maxwellian

LOCATION: BCAM Seminar room and Online

Abstract
We consider the Vlasov-Poisson-Boltzmann system without angular cutoff and the Vlasov-Poisson-Landau system with Coulomb potential near a global Maxwellian. We establish the global existence, uniqueness and large time behavior for solutions in a polynomial-weighted Sobolev space $H^2_{x,v}(⟨v⟩k)$ for some constant k > 0. For the domain union of cubes, we will consider the specular-reflection boundary condition and its high-order compatible specular boundary condition. The proof is based on extra dissipation generated from the semigroup method and energy estimates on electrostatic fields. It is a joint work with Chuqi Cao and Dingqun Deng (Tsinghua University).


Link to the session: 
https://us06web.zoom.us/j/99649860282?pwd=SE0vemtYMFlwbFBNTXQyOTBONG0vZz09

More info at https://sites.google.com/view/apdebilbao/home